(a) Field of the Invention
The present invention relates to a method for decoding channel codes. More specifically, the present invention relates to a method and device for receiving data coded with RM (Reed-Muller) codes through a channel having continuous output values, and decoding the data through a soft decision decoding method using a decision by majority.
(b) Description of the Related Art
In 1954, Muller initially described the RM codes using binary functions, and in the same year, Reed found that the RM codes are expressed as multinomials of a binary field. This important feature makes it possible to decode the original codes using the decision by majority.
The RM codes are more flexible in that they may control a number of errors per codeword as opposed to the existing Hamming codes and the Golay codes, and hence they have been used to various applications. For example, 32-bit first-order RM codes were applied to the communication system of the spaceship Mariner launched in 1969, and the RM codes became a theoretical basis for various channel codes because of combinational and mathematical features provided by the definition of the RM codes.
However, the RM codes were not applied to the spaceship Pioneer since convolutional codes and sequential decoding were discovered, and they lost popularity since it was found that the BCH codes and the Reed Solomon codes outperform the RM codes.
As it has been found that short or first-order RM codes have a minimum length that is identical with that of the BCH codes and they have a very fast maximum likelihood decoding method that is not found in the BCH codes, data transmission rates have been newly applied to fields that require high-speed coding and decoding from the fields that have almost reached their technical limits.
The maximum likelihood fast decoding method found from the RM codes was proposed by Reed, and it is accordingly referred to as the Reed decoding method. The Reed decoding method is a method for correcting and decoding a plurality of errors by using a set of codewords generating equations of the RM codes, that is, it uses decision by majority which is the simplest decoding format. In the case of general codes, the decision by majority is known to be fast but suboptimal, but it is also found to be the maximum likelihood decoding method for the RM codes.
The decision by majority uses estimates of information bits encoded by an encoder from the codewords to be decoded. At least one estimate of the respective information bits may be calculated from the codeword-generating equations. Since many candidates are provided for an identical information bit, the decision by majority is performed on them, and a value of the corresponding bit is determined using the values of 0 or 1 more frequently provided.
Since the codeword-generating equation of the RM codes is defined to be product and sum of regular and simple codes known as the Hadamard codes, the format of the codeword-generating equation is very regular. Hence, a method for obtaining estimates of the information bits from the set of equations is also regular, and when a method for calculating a single estimate candidate is provided, other estimate candidates may be calculated by performing the same calculation on the bits corresponding to an index obtained by adding a predetermined number to a bit index of the codeword used for the first candidate, thereby enabling high-speed decoding.
The Reed decoding method is a maximum likelihood decoding method for high-speed decoding as described above, but since an area for defining calculation related to the decoding method is a binary field, and decoding inputs received through a channel have continuous values, the continuous values are to be converted into binary numbers of 0 and 1 so as to perform the calculation defined in the binary field. In this process, a hard decision for determining corresponding numbers according to codes of the decoder inputs is performed.
A binary field calculation is then performed on the received codeword on which the hard decision is performed to thereby obtain each bit's estimate candidate. The number of respective estimate candidates is determined according to a degree of the RM codes, and the more degrees the RM codes have, the more the number of the estimate candidates increases. The obtained candidates have one of the values 0 and 1, and the corresponding bit is decoded to the value that has more candidates.
The Reed decoding method requires previous performance of a hard decision since it calculates the binary field when obtaining information bit estimates for decision by majority. That is, since the value of the corresponding codeword bit is determined only through input codes of a decoder, the decision according to the input codes of the decoder in the case of a channel with low reliability of the input values of the decoder generates errors for each codeword bit. This reduces the decoder's decoding performance to lower total error correction performance. Also, it is unavoidable that bit errors may be generated with a high probability of ½ when the number of the candidates of decision by majority is even and both values of 0 and 1 have received the same number of votes, and accordingly, codeword patterns that may not be decodable may exist.
A prior art discloses an RM encoding and decoding method for decoding reliability of the codeword configured according to encoding by perforation and zero padding to thereby be applied to variable-length codewords, but it also requires a hard decision on the inputs, thereby failing to solve the above-noted problem.